Surrogate modeling for dynamic analysis of an uncertain notched rotor system and roles of Chebyshev parameters

The non-intrusive Chebyshev surrogate coupled with the harmonic balance method is developed to calculate harmonics and super-harmonic responses of an uncertain notched rotor, i.e., rotor with an open crack. The deterministic rotor model is formulated by the finite element method and an open crack in the elastic shaft introduces the asymmetry fault. A large size crack in the middle span of the shaft is considered, which makes the system susceptible to variations of parameters. The scanning approach is used to validate the accuracy of the surrogate function. Importantly, roles of Chebyshev parameters on performance are studied and proved. It is found that the Chebyshev order is the crucial factor to reduce the spurious peaks and overestimation near critical speeds of the rotor model. An improved surrogate function with fewer collocations is formulated to solve uncertain problems with many uncertainties and high orders are required in surrogate models. It is found that the surrogate function can efficiently and accurately estimate the uncertain responses of the notched rotor with multi-interval variables. The results will benefit interval uncertainty analysis of general large-scale and sensitive mechanical systems.